Pre-Algebra Examples

${(\frac{4}{3})}^{2} \div (\frac{4}{3} - \frac{1}{9})$

Step 1

Rewrite the division as a fraction.

$\frac{{(\frac{4}{3})}^{2}}{\frac{4}{3} - \frac{1}{9}}$

Step 2

Simplify the numerator.

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Step 2.1

Apply the product rule to $\frac{4}{3}$ .

$\frac{\frac{4^{2}}{3^{2}}}{\frac{4}{3} - \frac{1}{9}}$

Step 2.2

Raise $4$ to the power of $2$ .

$\frac{\frac{16}{3^{2}}}{\frac{4}{3} - \frac{1}{9}}$

Step 2.3

Raise $3$ to the power of $2$ .

$\frac{\frac{16}{9}}{\frac{4}{3} - \frac{1}{9}}$

Step 3

Simplify the denominator.

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Step 3.1

To write $\frac{4}{3}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{\frac{16}{9}}{\frac{4}{3} \cdot \frac{3}{3} - \frac{1}{9}}$

Step 3.2

Write each expression with a common denominator of $9$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.2.1

Multiply $\frac{4}{3}$ by $\frac{3}{3}$ .

$\frac{\frac{16}{9}}{\frac{4 \cdot 3}{3 \cdot 3} - \frac{1}{9}}$

Step 3.2.2

Multiply $3$ by $3$ .

$\frac{\frac{16}{9}}{\frac{4 \cdot 3}{9} - \frac{1}{9}}$

Step 3.3

Combine the numerators over the common denominator.

$\frac{\frac{16}{9}}{\frac{4 \cdot 3 - 1}{9}}$

Step 3.4

Simplify the numerator.

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Step 3.4.1

Multiply $4$ by $3$ .

$\frac{\frac{16}{9}}{\frac{12 - 1}{9}}$

Step 3.4.2

Subtract $1$ from $12$ .

$\frac{\frac{16}{9}}{\frac{11}{9}}$

Step 4

Multiply the numerator by the reciprocal of the denominator.

$\frac{16}{9} \cdot \frac{9}{11}$

Step 5

Cancel the common factor of $9$ .

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Step 5.1

Cancel the common factor.

$\frac{16}{9} \cdot \frac{9}{11}$

Step 5.2

Rewrite the expression.

$16 (\frac{1}{11})$

Step 6

Combine $16$ and $\frac{1}{11}$ .

$\frac{16}{11}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{16}{11}$

Decimal Form:

$1.\overline{45}$

Mixed Number Form:

$1 \frac{5}{11}$